Kalmbach implication in orthomodular posets
| Authors | |
|---|---|
| Year of publication | 2023 |
| Type | Article in Proceedings |
| Conference | 53rd International Symposium on Multiple-Valued Logic (ISMVL 2023) |
| MU Faculty or unit | |
| Citation | |
| Web | http://dx.doi.org/10.1109/ismvl57333.2023.00015 |
| Doi | http://dx.doi.org/10.1109/ISMVL57333.2023.00015 |
| Keywords | multiple-valued implication; classical implication; Kalmbach implication; non-tolens implication; orthomodular poset; modus ponens rule |
| Description | We show that for every orthogonal lub-complete poset P = (P,?,', 0, 1), we can introduce multiple-valued implications sharing properties with quantum implications presented for orthomodular lattices by Kalmbach. We call them classical implication, Kalmbach implication, and non-tolens implication.If the classical implication satisfies the order property, then the corresponding orthologic becomes classical and vice versa. If the Kalmbach or non-tolens implication meets the order property, then the corresponding orthologic becomes quantum and vice versa. A related result for the modus ponens rule is obtained. |
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